Forward discrete wavelet transform: implement periodic symmetric extension at boundaries

[GoogleCodeExporter]

According to the final draft
of 15444-1, section F.2 (normative), the inverse wavelet transform must
use periodic symmetric extension at boundaries. 

I assume that this is also required for the forward wavelet.

However, openjpeg code truncates at the boundaries:

#define OPJ_S_(i) ((i)<0?OPJ_S(0):((i)>=sn?OPJ_S(sn-1):OPJ_S(i)))
#define OPJ_D_(i) ((i)<0?OPJ_D(0):((i)>=dn?OPJ_D(dn-1):OPJ_D(i)))

Symmetric extension should reduce boundary artifacts.

Original issue reported on code.google.com by boxe...@gmail.com on 18 Dec 2014 at 9:35

[GoogleCodeExporter]

Since part 1 uses full-sample symmetric wavelets, the symmetric border 
extension operation commutes with the transform operation. 

So, if S is the symmetric extension operation, F is the forward transform, and 
R is the reverse transform, then we have the standard requiring

Decoded Image =  R(S(F(Original Image)))

Because S and F are commutative, and S * S = S, we get

Decoded Image = R(S(F(S(Original Image))))

So, we must use the symmetric extension in the forward transform as well.

Therefore, if my reading of the standard is correct, we should not be clamping 
the image at the border, as we are doing in the above macros. We should use 
symmetric extension.

Original comment by boxe...@gmail.com on 20 Dec 2014 at 3:07

• Added labels: Type-Defect
• Removed labels: Type-Enhancement

[GoogleCodeExporter]

This being related to the standard, i'll cc antonin.

Original comment by m.darb...@gmail.com on 20 Dec 2014 at 3:15

[GoogleCodeExporter]

By the way, this is not a conformance issue after all: encoder conformance 
relates completely to the syntax of the code stream, and not the encoded 
pixels. 

See ISO/IEC 15444-4 Annex F.1
http://www.openjpeg.org/conformance/T.803e.pdf

Nevertheless, clamping at the boundary still does introduce artifacts at the 
boundary. So, this is not a desirable feature;

Original comment by boxe...@gmail.com on 21 Dec 2014 at 5:05